Optimized aerodynamic profile for a turbine vane, in particular for a nozzle of a turbine

ABSTRACT

When cold and in the non-coated state, the aerodynamic profile is substantially identical to a nominal profile determined by the Cartesian coordinates X,Y, Zadim given in Table 1, in which the coordinate Zadim is the quotient D/H where D is the distance of the point under consideration from a first reference plane P0 situated at the base of the nominal profile, and H is the height of said profile measured from the first reference plane to a second reference plane P1. The measurements D and H are taken radially relative to the axis of the turbine, while the X coordinate is measured in the axial direction of the turbine.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims the benefit of priority to U.S. Patent Application No. 62/504,557, filed on May 11, 2017, the entirety of which is incorporated by reference herein.

INTRODUCTION

The present disclosure relates to an aerodynamic profile for a turbine vane.

In particular, the disclosure relates to the aerodynamic profile of a nozzle vane forming a portion of the stator of a gas turbine, and more particularly of a low pressure turbine of the type used in a turbojet of an aircraft.

The disclosure relates in particular to a nozzle vane of a turbine having a plurality of stages, preferably five stages.

Such a profile should enable the turbine to provide the desired efficiency, and in order to do that it must be such that the flow of air around the profile is sound over the working spectrum of the turbine, i.e. substantially such that it does not give rise to turbulence, which is harmful for overall efficiency.

It must be capable of being installed properly in the environment of the engine, and in particular, for a nozzle vane forming a portion of the stator of the turbine, it must be capable of being fastened easily to the sectors of the foot platform (the zone of the vane that is furthest from the axis of rotation of the turbine) and of the head platform (the zone that is closest to said axis). Furthermore, this part must present a profile enabling it to be manufactured in a reliable and cost-effective manner by available manufacturing methods, such as casting, forging, machining, additive fabrication, or else weaving, without this list being limitative.

Furthermore, the profile of the vane must enable it to withstand the mechanical stresses, to which the vane is subjected, by enabling those stresses to be spread over the entire vane in such a manner as to avoid premature wear thereof. This spreading must apply both in static mode and in dynamic mode.

An object of the disclosure is to propose an aerodynamic profile for a turbine vane that is optimized, and capable of satisfying those objectives.

This object is achieved by the fact that when cold and in a non-coated state, said profile is substantially identical to a nominal profile determined by the Cartesian coordinates X,Y,Zadim given in Table 1, in which the coordinate Zadim is the quotient D/H where D is the distance of the point P under consideration from a reference X,Y plane situated at the base of the nominal profile, and H is the height of said profile measured from said reference plane that is the intersection of the stacking axis of the vane and the axisymmetric surface of the hub, out to a second reference plane that is the intersection of said stacking axis with the axisymmetric surface of the casing, the measurements D and H being taken radially relative to the axis of the turbine, while the coordinate X is measured in the axial direction of the turbine.

This profile has been determined as a result of numerous tests and simulations. It is defined cold, i.e. at an ambient temperature of 20° C. That is a reference temperature at which the profile is geometrically determined. The above-mentioned objectives of aerodynamics and mechanical optimization are naturally valid for the conditions of use of this aerodynamic profile, i.e. when hot, at a temperature that is stabilized when the engine of which the turbine forms a part is being used under cruising conditions.

Furthermore, the aerodynamic profile of the disclosure is defined in the non-coated state. Since turbine vanes are subjected to high temperature gradients, it is common practice for them to be provided with a coating having thermal properties enabling them more easily to withstand such temperature variations. The profile is determined prior to installing such a coating.

It is stated above that the profile of the disclosure is “substantially identical” to the nominal profile. This means that the profile may depart very slightly from said nominal profile.

The aerodynamic profile is thus preferably defined within an envelope of ±1 millimeter (mm) in a direction normal to the surface of the nominal profile.

It is also preferable for the X,Y coordinates of the aerodynamic profile to lie within a range of ±5% relative to the X,Y coordinates of the nominal profile.

In addition, the aerodynamic profile may be positioned rotated within ±10°, particularly within ±5°, more particularly within ±3°, with respect to the radial axis of the vane, along which the coordinate Zadim is measured.

These variations take account in particular to at least one of manufacturing tolerances of the profile, the setting of the profile to adapt to the environment when in operation, and possible deformation occurring when mounting the vane and integrating the same in the nozzle.

With a nozzle vane, i.e. a portion of the stator of a turbine, the profile serves to orient the fluid correctly for the turbine blades that are situated downstream, and that belong in particular to the rotary wheel of the same stage of the turbine.

BRIEF DESCRIPTION OF THE DRAWINGS

The disclosure can be better understood and its advantages appear better on reading the following detailed description of an embodiment given by way of non-limiting example. The description refers to the accompanying drawings, in which:

FIG. 1 is a fragmentary axial diagrammatic section view of a turbine including a vane of profile that corresponds to that of the present disclosure;

FIG. 2 shows a vane of the turbine.

DETAILED DESCRIPTION

The turbine shown in axial section in FIG. 1 comprises five stages referenced respectively S1 to S5. In the direction DF going from upstream to downstream, each stage comprises a nozzle that forms a portion of the stator of the turbine and that has a plurality of radially-oriented vanes, and a rotary wheel that forms a portion of the rotor of the turbine and that likewise includes a plurality of radially-oriented blades.

In FIG. 1, the vanes of the nozzles of stages S1 to S5 are given references N1 to N5 (these vanes are shown in dashed lines, for ease of representation), whereas the blades of rotary wheels of stages S1 to S5 are given respective references W1 to W5.

In known manner, the vanes of the nozzles are fastened at both ends to stationary structure portions, while the blades of the rotary wheels are fastened to a rotary disk via their roots that are formed at their radially-inner ends closer to the axis of the rotation A of the turbine. The disks forming parts of the wheels W1 to W5 are constrained to rotate together.

The disclosure relates a vane of one of the nozzles of the turbine that, as mentioned above, preferably comprises five stages as shown, without this number being limiting.

As best seen in FIG. 2, via its foot 10, which is its end remote from the axis of rotation A, the vane is fastened to the outer ring of the turbine, which ring is stationary in rotation. Via its head 14, formed by its end closer to the axis of rotation A, the vane is fastened to an inner shroud of the turbine. By convention, the aerodynamic profile 18 of the vane is the entire portion of said vane that extends radially outwards from its head 14 to its foot 10 without incorporating the fastenings respectively to the outer ring and to the inner shroud.

In FIG. 2, there can be seen a frame of reference comprising Cartesian coordinates X,Y,Z. The radial direction Z is the height direction of the vane, which extends radially from its head to its foot. This direction Z is perpendicular to the axial direction X which is the direction of the axis of rotation A of the turbine. The direction Y is perpendicular to the X,Z plane and is therefore tangential to the direction of rotation of the turbine.

The nominal profile from which the aerodynamic profile of the disclosure is determined is defined in following Table 1 of coordinates, in which the coordinate Zadim, measured along the axis Z is non-dimensional, whereas the dimensions X and Y, respectively measured along the axes X and Y, are expressed in millimeters.

TABLE 1 X Y Zadim −9.77546 6.082523 −0.14999 −9.81288 6.0459 −0.14999 −9.85767 5.984329 −0.14999 −9.90577 5.877182 −0.14999 −9.94043 5.71733 −0.14999 −9.94892 5.503779 −0.14999 −9.92356 5.238265 −0.14999 −9.85895 4.922781 −0.14999 −9.75109 4.559872 −0.14999 −9.59672 4.152358 −0.14999 −9.39275 3.703716 −0.14999 −9.13576 3.218465 −0.14999 −8.82186 2.702469 −0.14999 −8.44662 2.163334 −0.14999 −8.00524 1.610744 −0.14999 −7.49191 1.057628 −0.14999 −6.89971 0.521872 −0.14999 −6.22139 0.028544 −0.14999 −5.45161 −0.38687 −0.14999 −4.59251 −0.67746 −0.14999 −3.67004 −0.7908 −0.14999 −2.72075 −0.69012 −0.14999 −1.80102 −0.37697 −0.14999 −0.95085 0.112518 −0.14999 −0.18459 0.734079 −0.14999 0.498873 1.446115 −0.14999 1.107698 2.216363 −0.14999 1.652228 3.020582 −0.14999 2.145227 3.838909 −0.14999 2.596476 4.657022 −0.14999 3.011337 5.464987 −0.14999 3.393456 6.254822 −0.14999 3.746764 7.019201 −0.14999 4.074725 7.751704 −0.14999 4.379382 8.447137 −0.14999 4.661168 9.101534 −0.14999 4.918885 9.712138 −0.14999 5.152303 10.27633 −0.14999 5.362247 10.79162 −0.14999 5.549183 11.25637 −0.14999 5.713711 11.66952 −0.14999 5.856474 12.03074 −0.14999 5.978151 12.34048 −0.14999 6.079589 12.59993 −0.14999 6.16184 12.81104 −0.14999 6.225742 12.97682 −0.14999 6.239435 13.10891 −0.14999 6.205176 13.19518 −0.14999 6.16751 13.23986 −0.14999 6.131133 13.26615 −0.14999 6.097113 13.28143 −0.14999 6.049472 13.29109 −0.14999 5.973248 13.28067 −0.14999 5.882516 13.21719 −0.14999 5.810481 13.0883 −0.14999 5.720087 12.92309 −0.14999 5.608639 12.72013 −0.14999 5.475109 12.47788 −0.14999 5.318677 12.19546 −0.14999 5.138779 11.87255 −0.14999 4.935185 11.50935 −0.14999 4.707046 11.10702 −0.14999 4.453477 10.66741 −0.14999 4.174384 10.19244 −0.14999 3.870024 9.684417 −0.14999 3.540797 9.146017 −0.14999 3.186799 8.580585 −0.14999 2.808007 7.991988 −0.14999 2.404958 7.384158 −0.14999 1.977929 6.761582 −0.14999 1.525379 6.130425 −0.14999 1.04588 5.497353 −0.14999 0.539117 4.868804 −0.14999 0.003138 4.253232 −0.14999 −0.56594 3.662102 −0.14999 −1.17305 3.110422 −0.14999 −1.82177 2.616277 −0.14999 −2.51417 2.203614 −0.14999 −3.24835 1.906 −0.14999 −4.01037 1.758706 −0.14999 −4.76196 1.782116 −0.14999 −5.46565 1.965029 −0.14999 −6.09372 2.267055 −0.14999 −6.64141 2.641551 −0.14999 −7.1143 3.053337 −0.14999 −7.52134 3.477334 −0.14999 −7.87162 3.896075 −0.14999 −8.17342 4.297229 −0.14999 −8.43356 4.67222 −0.14999 −8.65868 5.014449 −0.14999 −8.85626 5.318022 −0.14999 −9.0301 5.580326 −0.14999 −9.18583 5.797994 −0.14999 −9.32902 5.967187 −0.14999 −9.46187 6.084345 −0.14999 −9.58625 6.140964 −0.14999 −9.6833 6.135584 −0.14999 −12.2955 5.207186 −0.07499 −12.3332 5.167108 −0.07499 −12.3775 5.100395 −0.07499 −12.4225 4.985393 −0.07499 −12.449 4.815527 −0.07499 −12.4429 4.590917 −0.07499 −12.3962 4.314343 −0.07499 −12.3041 3.988561 −0.07499 −12.1628 3.616437 −0.07499 −11.9692 3.201189 −0.07499 −11.7202 2.746788 −0.07499 −11.4124 2.258385 −0.07499 −11.0418 1.742712 −0.07499 −10.604 1.208521 −0.07499 −10.0943 0.667085 −0.07499 −9.50699 0.133561 −0.07499 −8.83599 −0.37122 −0.07499 −8.07605 −0.81862 −0.07499 −7.22616 −1.17013 −0.07499 −6.29627 −1.38049 −0.07499 −5.31981 −1.40426 −0.07499 −4.33167 −1.21562 −0.07499 −3.3907 −0.82154 −0.07499 −2.52868 −0.25509 −0.07499 −1.76221 0.443849 −0.07499 −1.09001 1.234237 −0.07499 −0.50057 2.081563 −0.07499 0.019481 2.960305 −0.07499 0.486094 3.849792 −0.07499 0.912106 4.734936 −0.07499 1.304419 5.605559 −0.07499 1.667278 6.453707 −0.07499 2.004658 7.272269 −0.07499 2.320182 8.054879 −0.07499 2.615925 8.796333 −0.07499 2.892096 9.492673 −0.07499 3.145813 10.14167 −0.07499 3.375808 10.741 −0.07499 3.582936 11.28813 −0.07499 3.767557 11.78139 −0.07499 3.93019 12.21975 −0.07499 4.071412 12.60293 −0.07499 4.191858 12.93143 −0.07499 4.29232 13.20655 −0.07499 4.373812 13.43039 −0.07499 4.437335 13.60604 −0.07499 4.45338 13.74469 −0.07499 4.416831 13.83507 −0.07499 4.375977 13.88102 −0.07499 4.336705 13.90718 −0.07499 4.300474 13.92149 −0.07499 4.250244 13.92894 −0.07499 4.171488 13.91337 −0.07499 4.081924 13.84006 −0.07499 4.011577 13.70283 −0.07499 3.92325 13.52708 −0.07499 3.814447 13.31109 −0.07499 3.684192 13.05321 −0.07499 3.53174 12.75243 −0.07499 3.356591 12.40836 −0.07499 3.158524 12.02119 −0.07499 2.93634 11.59225 −0.07499 2.688538 11.12366 −0.07499 2.414832 10.61753 −0.07499 2.115247 10.07636 −0.07499 1.789921 9.503091 −0.07499 1.438678 8.901324 −0.07499 1.061385 8.275126 −0.07499 0.658423 7.628678 −0.07499 0.229774 6.966831 −0.07499 −0.22599 6.295795 −0.07499 −0.71007 5.622209 −0.07499 −1.22288 4.952737 −0.07499 −1.76615 4.295723 −0.07499 −2.34266 3.661534 −0.07499 −2.95611 3.063292 −0.07499 −3.60966 2.516876 −0.07499 −4.30582 2.043021 −0.07499 −5.04499 1.670653 −0.07499 −5.81891 1.432469 −0.07499 −6.60146 1.353542 −0.07499 −7.35498 1.437256 −0.07499 −8.05027 1.654468 −0.07499 −8.67133 1.962469 −0.07499 −9.21751 2.324053 −0.07499 −9.6939 2.711275 −0.07499 −10.1075 3.103784 −0.07499 −10.4657 3.486726 −0.07499 −10.7751 3.849366 −0.07499 −11.0423 4.183461 −0.07499 −11.2755 4.481401 −0.07499 −11.4783 4.740053 −0.07499 −11.6577 4.954444 −0.07499 −11.8194 5.120098 −0.07499 −11.9669 5.231869 −0.07499 −12.1012 5.2801 −0.07499 −12.2019 5.267125 −0.07499 −14.7492 4.233751 0 −14.7873 4.190257 0 −14.831 4.118454 0 −14.8729 3.995703 0 −14.8913 3.816149 0 −14.8704 3.581083 0 −14.8025 3.29444 0 −14.6832 2.959565 0 −14.5089 2.579629 0 −14.2767 2.15822 0 −13.9835 1.6998 0 −13.626 1.210168 0 −13.2001 0.696938 0 −12.7017 0.170044 0 −12.126 −0.35762 0 −11.4679 −0.86872 0 −10.7225 −1.33978 0 −9.88692 −1.73917 0 −8.96448 −2.02685 0 −7.97389 −2.16016 0 −6.94795 −2.10063 0 −5.92697 −1.8305 0 −4.96424 −1.36055 0 −4.08975 −0.72128 0 −3.32172 0.051183 0 −2.6597 0.916572 0 −2.08922 1.838248 0 −1.59366 2.789207 0 −1.154 3.748067 0 −0.75392 4.698943 0 −0.38472 5.631345 0 −0.04141 6.537265 0 0.279983 7.40973 0 0.58329 8.242357 0 0.870233 9.03002 0 1.141351 9.768505 0 1.392049 10.45601 0 1.619534 11.09061 0 1.824699 11.66971 0 2.007816 12.19161 0 2.169297 12.65531 0 2.30965 13.06056 0 2.42945 13.40791 0 2.529438 13.69879 0 2.610583 13.93542 0 2.673985 14.12104 0 2.692625 14.26641 0 2.654063 14.36106 0 2.610047 14.40838 0 2.567899 14.43445 0 2.52947 14.44783 0 2.476692 14.45314 0 2.395467 14.43258 0 2.307326 14.34975 0 2.238396 14.20418 0 2.151765 14.01788 0 2.045155 13.78887 0 1.917644 13.51535 0 1.768564 13.19623 0 1.597487 12.83104 0 1.40418 12.41997 0 1.1871 11.96446 0 0.94411 11.46695 0 0.674735 10.92968 0 0.378776 10.35535 0 0.056102 9.747139 0 −0.29373 9.108928 0 −0.67095 8.444968 0 −1.07534 7.759713 0 −1.50725 7.058391 0 −1.968 6.34732 0 −2.45857 5.633145 0 −2.97948 4.922812 0 −3.53232 4.224696 0 −4.11887 3.548368 0 −4.74158 2.905467 0 −5.40301 2.310163 0 −6.10566 1.780783 0 −6.85107 1.342486 0 −7.63394 1.024619 0 −8.43861 0.853669 0 −9.23004 0.84269 0 −9.97934 0.973408 0 −10.6639 1.210117 0 −11.276 1.516011 0 −11.8164 1.861345 0 −12.2894 2.223334 0 −12.7009 2.584678 0 −13.0573 2.932424 0 −13.3651 3.256443 0 −13.6323 3.547513 0 −13.8631 3.801708 0 −14.0653 4.012359 0 −14.2449 4.174294 0 −14.4063 4.280594 0 −14.5499 4.320539 0 −14.6541 4.300384 0 −17.3292 4.885935 0.100006 −17.373 4.843084 0.100006 −17.425 4.770718 0.100006 −17.4783 4.644022 0.100006 −17.5086 4.455238 0.100006 −17.4977 4.205311 0.100006 −17.4376 3.899071 0.100006 −17.3237 3.539995 0.100006 −17.1527 3.13142 0.100006 −16.9213 2.677141 0.100006 −16.6258 2.181973 0.100006 −16.2624 1.652221 0.100006 −15.8261 1.09627 0.100006 −15.3118 0.525139 0.100006 −14.7137 −0.0467 0.100006 −14.0255 −0.59989 0.100006 −13.2417 −1.10865 0.100006 −12.3598 −1.53918 0.100006 −11.3841 −1.85087 0.100006 −10.3376 −2.00302 0.100006 −9.24666 −1.96024 0.100006 −8.15905 −1.70291 0.100006 −7.12044 −1.2454 0.100006 −6.15983 −0.61726 0.100006 −5.29775 0.150458 0.100006 −4.53774 1.019846 0.100006 −3.8675 1.95284 0.100006 −3.27151 2.920455 0.100006 −2.7328 3.899932 0.100006 −2.2346 4.872984 0.100006 −1.76762 5.82755 0.100006 −1.32732 6.754918 0.100006 −0.91097 7.647865 0.100006 −0.51566 8.49961 0.100006 −0.14005 9.304597 0.100006 0.215459 10.0586 0.100006 0.545764 10.76016 0.100006 0.847492 11.40767 0.100006 1.120714 11.99858 0.100006 1.365482 12.53111 0.100006 1.581972 13.00423 0.100006 1.770567 13.4177 0.100006 1.931836 13.77208 0.100006 2.06663 14.06882 0.100006 2.176138 14.31023 0.100006 2.261888 14.49956 0.100006 2.301148 14.64983 0.100006 2.271679 14.75381 0.100006 2.229479 14.80782 0.100006 2.186974 14.83866 0.100006 2.147072 14.85557 0.100006 2.091312 14.86456 0.100006 2.003788 14.84721 0.100006 1.907076 14.7623 0.100006 1.821354 14.61373 0.100006 1.712967 14.42366 0.100006 1.579733 14.18996 0.100006 1.420569 13.91077 0.100006 1.234754 13.58493 0.100006 1.021875 13.21195 0.100006 0.781697 12.79202 0.100006 0.512676 12.32687 0.100006 0.212958 11.8191 0.100006 −0.11779 11.27114 0.100006 −0.47972 10.68596 0.100006 −0.87294 10.06711 0.100006 −1.29783 9.418899 0.100006 −1.7543 8.745881 0.100006 −2.24202 8.052975 0.100006 −2.76139 7.346152 0.100006 −3.31319 6.632227 0.100006 −3.89753 5.918161 0.100006 −4.51466 5.211686 0.100006 −5.16532 4.521799 0.100006 −5.8496 3.857976 0.100006 −6.56763 3.231162 0.100006 −7.31979 2.65473 0.100006 −8.10639 2.145791 0.100006 −8.92644 1.726706 0.100006 −9.77352 1.422789 0.100006 −10.6333 1.258533 0.100006 −11.4775 1.248013 0.100006 −12.276 1.37887 0.100006 −13.0085 1.621017 0.100006 −13.6637 1.940152 0.100006 −14.2415 2.304173 0.100006 −14.7461 2.688547 0.100006 −15.1831 3.074871 0.100006 −15.5591 3.448752 0.100006 −15.8816 3.798722 0.100006 −16.1596 4.114659 0.100006 −16.3978 4.391969 0.100006 −16.6061 4.622871 0.100006 −16.7913 4.801903 0.100006 −16.9596 4.920388 0.100006 −17.1114 4.966529 0.100006 −17.2232 4.949731 0.100006 −19.852 3.546479 0.200005 −19.8949 3.500029 0.200005 −19.9449 3.422927 0.200005 −19.9937 3.28974 0.200005 −20.0143 3.093362 0.200005 −19.9866 2.836737 0.200005 −19.9019 2.525988 0.200005 −19.7558 2.165669 0.200005 −19.5452 1.759943 0.200005 −19.2668 1.313414 0.200005 −18.9172 0.831859 0.200005 −18.4923 0.322791 0.200005 −17.9878 −0.20393 0.200005 −17.399 −0.73538 0.200005 −16.721 −1.25471 0.200005 −15.9495 −1.73969 0.200005 −15.0821 −2.16131 0.200005 −14.1215 −2.48276 0.200005 −13.0814 −2.66183 0.200005 −11.9882 −2.65956 0.200005 −10.88 −2.45306 0.200005 −9.80246 −2.04653 0.200005 −8.78838 −1.46033 0.200005 −7.85863 −0.72615 0.200005 −7.02209 0.122417 0.200005 −6.27676 1.052539 0.200005 −5.6109 2.033575 0.200005 −5.0113 3.041611 0.200005 −4.46532 4.057911 0.200005 −3.96123 5.067253 0.200005 −3.49192 6.058501 0.200005 −3.05321 7.022899 0.200005 −2.64289 7.953262 0.200005 −2.25814 8.842729 0.200005 −1.89708 9.685423 0.200005 −1.55969 10.47684 0.200005 −1.24825 11.21405 0.200005 −0.96362 11.89415 0.200005 −0.70551 12.51449 0.200005 −0.47402 13.07332 0.200005 −0.26908 13.56965 0.200005 −0.09039 14.00329 0.200005 0.062493 14.37491 0.200005 0.190346 14.68604 0.200005 0.294257 14.93912 0.200005 0.375669 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3.764251 0.800003 −20.6481 3.628435 0.800003 −20.6866 3.426789 0.800003 −20.6799 3.158718 0.800003 −20.6088 2.831614 0.800003 −20.4612 2.455519 0.800003 −20.2298 2.040626 0.800003 −19.9102 1.597022 0.800003 −19.4987 1.135394 0.800003 −18.9926 0.667886 0.800003 −18.3896 0.208824 0.800003 −17.6886 −0.22459 0.800003 −16.89 −0.61168 0.800003 −15.9975 −0.92801 0.800003 −15.0195 −1.1458 0.800003 −13.9713 −1.23563 0.800003 −12.8758 −1.17093 0.800003 −11.7643 −0.93371 0.800003 −10.6693 −0.52189 0.800003 −9.61862 0.051257 0.800003 −8.62986 0.76151 0.800003 −7.71081 1.580941 0.800003 −6.86173 2.482458 0.800003 −6.0783 3.441938 0.800003 −5.35428 4.438918 0.800003 −4.6838 5.456752 0.800003 −4.06213 6.481807 0.800003 −3.48336 7.501365 0.800003 −2.94249 8.504498 0.800003 −2.43639 9.482235 0.800003 −1.96343 10.42709 0.800003 −1.52133 11.33189 0.800003 −1.10878 12.19059 0.800003 −0.72557 12.9983 0.800003 −0.37172 13.75087 0.800003 −0.04725 14.44488 0.800003 0.247612 15.07774 0.800003 0.512573 15.64771 0.800003 0.747531 16.15382 0.800003 0.952635 16.59593 0.800003 1.128306 16.97474 0.800003 1.27533 17.29185 0.800003 1.394896 17.54977 0.800003 1.488637 17.752 0.800003 1.538281 17.91093 0.800003 1.506684 18.02269 0.800003 1.459519 18.07888 0.800003 1.41242 18.10975 0.800003 1.366426 18.12634 0.800003 1.303043 18.13246 0.800003 1.205861 18.10531 0.800003 1.10677 18.00008 0.800003 1.013316 17.83061 0.800003 0.894124 17.61448 0.800003 0.747729 17.34866 0.800003 0.573007 17.031 0.800003 0.369218 16.66018 0.800003 0.135948 16.23558 0.800003 −0.12699 15.75739 0.800003 −0.41944 15.22644 0.800003 −0.74141 14.64442 0.800003 −1.09267 14.01361 0.800003 −1.47283 13.33691 0.800003 −1.88217 12.6182 0.800003 −2.32108 11.86202 0.800003 −2.78926 11.07313 0.800003 −3.28781 10.25758 0.800003 −3.81854 9.422503 0.800003 −4.38205 8.574853 0.800003 −4.97979 7.722756 0.800003 −5.61448 6.876041 0.800003 −6.28905 6.045774 0.800003 −7.00474 5.24305 0.800003 −7.7627 4.480446 0.800003 −8.56425 3.773087 0.800003 −9.40866 3.137333 0.800003 −10.2922 2.590332 0.800003 −11.2069 2.148994 0.800003 −12.14 1.828208 0.800003 −13.0733 1.637503 0.800003 −13.9851 1.577939 0.800003 −14.8528 1.639306 0.800003 −15.6585 1.802101 0.800003 −16.3911 2.040967 0.800003 −17.046 2.329268 0.800003 −17.6248 2.642261 0.800003 −18.1324 2.958802 0.800003 −18.5763 3.26081 0.800003 −18.9647 3.533737 0.800003 −19.306 3.765379 0.800003 −19.6082 3.943245 0.800003 −19.877 4.053647 0.800003 −20.1077 4.085776 0.800003 −20.2825 4.051422 0.800003 −20.3945 3.989616 0.800003 −18.4996 3.805586 0.900002 −18.5374 3.754123 0.900002 −18.5845 3.674241 0.900002 −18.6386 3.541644 0.900002 −18.6779 3.346087 0.900002 −18.6762 3.085556 0.900002 −18.6115 2.766802 0.900002 −18.4691 2.400997 0.900002 −18.2404 2.000073 0.900002 −17.9208 1.575713 0.900002 −17.5072 1.13985 0.900002 −16.9978 0.705523 0.900002 −16.3915 0.287633 0.900002 −15.6888 −0.09648 0.900002 −14.8922 −0.42662 0.900002 −14.0077 −0.67964 0.900002 −13.0461 −0.83027 0.900002 −12.024 −0.8531 0.900002 −10.9651 −0.72661 0.900002 −9.89922 −0.43809 0.900002 −8.85532 0.011534 0.900002 −7.85746 0.608634 0.900002 −6.92075 1.330902 0.900002 −6.05168 2.153052 0.900002 −5.25016 3.050479 0.900002 −4.51206 4.001103 0.900002 −3.83163 4.9861 0.900002 −3.20374 5.990164 0.900002 −2.62314 6.999965 0.900002 −2.08405 8.003427 0.900002 −1.58165 8.990208 0.900002 −1.11307 9.951828 0.900002 −0.67627 10.8809 0.900002 −0.26886 11.77051 0.900002 0.110555 12.6148 0.900002 0.462305 13.40901 0.900002 0.78657 14.1491 0.900002 1.083622 14.83163 0.900002 1.35324 15.45412 0.900002 1.595303 16.0148 0.900002 1.809802 16.51273 0.900002 1.996943 16.94771 0.900002 2.157163 17.32045 0.900002 2.29121 17.63249 0.900002 2.400197 17.8863 0.900002 2.485631 18.08531 0.900002 2.527249 18.24164 0.900002 2.492146 18.3489 0.900002 2.444606 18.40202 0.900002 2.398063 18.43079 0.900002 2.353239 18.44586 0.900002 2.291847 18.45078 0.900002 2.198056 18.42383 0.900002 2.101883 18.32233 0.900002 2.01549 18.15628 0.900002 1.905298 17.9445 0.900002 1.769868 17.6841 0.900002 1.608111 17.373 0.900002 1.419276 17.0099 0.900002 1.202918 16.59427 0.900002 0.958831 16.12629 0.900002 0.687053 15.6068 0.900002 0.387488 15.03746 0.900002 0.060444 14.42044 0.900002 −0.29389 13.7586 0.900002 −0.67571 13.05561 0.900002 −1.08544 12.31585 0.900002 −1.52282 11.54386 0.900002 −1.98875 10.74534 0.900002 −2.48495 9.927011 0.900002 −3.0121 9.095546 0.900002 −3.57143 8.258519 0.900002 −4.16549 7.425079 0.900002 −4.79713 6.605576 0.900002 −5.46783 5.810518 0.900002 −6.17882 5.051588 0.900002 −6.93166 4.342851 0.900002 −7.7263 3.699695 0.900002 −8.55999 3.138386 0.900002 −9.42624 2.675184 0.900002 −10.3139 2.324743 0.900002 −11.2067 2.097182 0.900002 −12.0846 1.994969 0.900002 −12.9259 2.010324 0.900002 −13.7123 2.126102 0.900002 −14.4322 2.319036 0.900002 −15.0797 2.563795 0.900002 −15.6548 2.836233 0.900002 −16.1616 3.115445 0.900002 −16.6068 3.382705 0.900002 −16.9981 3.623025 0.900002 −17.3431 3.823175 0.900002 −17.6494 3.968667 0.900002 −17.9206 4.043473 0.900002 −18.1455 4.037778 0.900002 −18.3067 3.976743 0.900002 −18.407 3.904114 0.900002 −15.9834 3.483343 1 −16.0151 3.430922 1 −16.0554 3.35144 1 −16.1027 3.222328 1 −16.1388 3.0342 1 −16.1382 2.784007 1 −16.0759 2.477958 1 −15.9345 2.128525 1 −15.704 1.749912 1 −15.38 1.355863 1 −14.9603 0.959849 1 −14.4447 0.575953 1 −13.8339 0.219606 1 −13.1308 −0.09194 1 −12.3406 −0.33944 1 −11.4721 −0.50186 1 −10.5391 −0.55748 1 −9.55978 −0.48619 1 −8.55836 −0.27287 1 −7.56154 0.088964 1 −6.59452 0.595167 1 −5.67715 1.231929 1 −4.82172 1.979213 1 −4.03312 2.814617 1 −3.31057 3.716282 1 −2.64974 4.664456 1 −2.04523 5.642313 1 −1.49241 6.636108 1 −0.98505 7.632995 1 −0.51729 8.621819 1 −0.0844 9.593069 1 0.316388 10.5389 1 0.687774 11.45216 1 1.032463 12.32627 1 1.352036 13.15571 1 1.647083 13.93594 1 1.918207 14.66296 1 2.165888 15.3335 1 2.390263 15.94508 1 2.591343 16.496 1 2.769276 16.98528 1 2.924349 17.41277 1 3.057005 17.77909 1 3.167922 18.08578 1 3.258061 18.33525 1 3.328693 18.53088 1 3.356525 18.68371 1 3.315109 18.78391 1 3.266369 18.83197 1 3.220231 18.85711 1 3.176783 18.86942 1 3.11802 18.87173 1 3.029241 18.84337 1 2.938742 18.7452 1 2.864656 18.58255 1 2.770181 18.37509 1 2.65394 18.12007 1 2.514927 17.81547 1 2.352411 17.46007 1 2.16591 17.05337 1 1.955184 16.59554 1 1.720117 16.08745 1 1.460578 15.53067 1 1.176651 14.92732 1 0.868466 14.2801 1 0.535784 13.59247 1 0.178105 12.86853 1 −0.20447 12.11258 1 −0.61272 11.32986 1 −1.04826 10.52651 1 −1.51211 9.708857 1 −2.00537 8.883782 1 −2.53046 8.059537 1 −3.09035 7.245528 1 −3.68711 6.451569 1 −4.32233 5.688331 1 −4.99818 4.968631 1 −5.71573 4.306821 1 −6.4738 3.718353 1 −7.26782 3.219026 1 −8.08874 2.823424 1 −8.92243 2.542414 1 −9.75055 2.37998 1 −10.5526 2.331039 1 −11.3099 2.381234 1 −12.0099 2.509812 1 −12.6449 2.693167 1 −13.2133 2.908038 1 −13.7176 3.133839 1 −14.1633 3.350976 1 −14.5568 3.54438 1 −14.9049 3.698895 1 −15.2135 3.79713 1 −15.481 3.820633 1 −15.6884 3.764812 1 −15.8249 3.672497 1 −15.9069 3.587438 1 −13.7684 3.872128 1.075001 −13.797 3.820335 1.075001 −13.8342 3.742839 1.075001 −13.8804 3.618424 1.075001 −13.9204 3.437884 1.075001 −13.9294 3.196509 1.075001 −13.88 2.899164 1.075001 −13.7519 2.558548 1.075001 −13.5338 2.190469 1.075001 −13.2207 1.810287 1.075001 −12.8113 1.432699 1.075001 −12.3059 1.072572 1.075001 −11.7066 0.745681 1.075001 −11.0177 0.469099 1.075001 −10.2459 0.261232 1.075001 −9.40156 0.141421 1.075001 −8.49928 0.128757 1.075001 −7.55792 0.23956 1.075001 −6.60051 0.484625 1.075001 −5.65083 0.866749 1.075001 −4.73089 1.380466 1.075001 −3.85797 2.012973 1.075001 −3.04323 2.746763 1.075001 −2.29141 3.561979 1.075001 −1.60214 4.438875 1.075001 −0.97174 5.359329 1.075001 −0.39574 6.307876 1.075001 0.129652 7.271728 1.075001 0.611094 8.238211 1.075001 1.054093 9.19672 1.075001 1.462969 10.13823 1.075001 1.840189 11.05529 1.075001 2.188791 11.94082 1.075001 2.511492 12.78849 1.075001 2.809873 13.59298 1.075001 3.084594 14.34988 1.075001 3.336485 15.05527 1.075001 3.566145 15.70595 1.075001 3.773837 16.2995 1.075001 3.959691 16.83424 1.075001 4.123948 17.30922 1.075001 4.266963 17.72423 1.075001 4.38921 18.0799 1.075001 4.491364 18.37768 1.075001 4.574341 18.61992 1.075001 4.639339 18.80987 1.075001 4.660761 18.9583 1.075001 4.617675 19.05372 1.075001 4.569725 19.09918 1.075001 4.524888 19.1229 1.075001 4.483065 19.13445 1.075001 4.4266 19.1367 1.075001 4.340978 19.11036 1.075001 4.251753 19.01819 1.075001 4.18222 18.86114 1.075001 4.09358 18.66083 1.075001 3.984398 18.41464 1.075001 3.853669 18.12066 1.075001 3.700629 17.77774 1.075001 3.524738 17.38543 1.075001 3.325742 16.9439 1.075001 3.10342 16.45403 1.075001 2.857615 15.91735 1.075001 2.588382 15.3359 1.075001 2.295839 14.71227 1.075001 1.979828 14.04974 1.075001 1.639927 13.35223 1.075001 1.276261 12.62383 1.075001 0.888297 11.86945 1.075001 0.474725 11.09483 1.075001 0.034492 10.30605 1.075001 −0.43319 9.509482 1.075001 −0.93035 8.712778 1.075001 −1.45972 7.924702 1.075001 −2.02347 7.154588 1.075001 −2.62319 6.412417 1.075001 −3.26104 5.710143 1.075001 −3.93849 5.061371 1.075001 −4.65507 4.48093 1.075001 −5.40714 3.984132 1.075001 −6.18665 3.585154 1.075001 −6.98063 3.294783 1.075001 −7.77176 3.117273 1.075001 −8.54083 3.048571 1.075001 −9.26979 3.075663 1.075001 −9.9457 3.179248 1.075001 −10.5609 3.336831 1.075001 −11.1134 3.525943 1.075001 −11.605 3.726249 1.075001 −12.0414 3.91754 1.075001 −12.4276 4.085809 1.075001 −12.7708 4.213203 1.075001 −13.0748 4.279986 1.075001 −13.3325 4.266091 1.075001 −13.5188 4.17652 1.075001 −13.6331 4.067276 1.075001 −13.7019 3.976985 1.075001 −11.4221 4.6359 1.149994 −11.4491 4.585619 1.149994 −11.4857 4.511206 1.149994 −11.5345 4.392863 1.149994 −11.5835 4.221436 1.149994 −11.6092 3.989825 1.149994 −11.5818 3.700487 1.149994 −11.4776 3.365324 1.149994 −11.2831 3.001329 1.149994 −10.9926 2.62549 1.149994 −10.6047 2.253818 1.149994 −10.1204 1.902063 1.149994 −9.54267 1.586434 1.149994 −8.87652 1.323943 1.149994 −8.12982 1.132309 1.149994 −7.31366 1.029467 1.149994 −6.44327 1.032296 1.149994 −5.53735 1.153993 1.149994 −4.61691 1.401739 1.149994 −3.703 1.775387 1.149994 −2.81451 2.268745 1.149994 −1.96662 2.870523 1.149994 −1.17005 3.566148 1.149994 −0.43009 4.33848 1.149994 0.25259 5.169882 1.149994 0.880429 6.043746 1.149994 1.456501 6.945829 1.149994 1.983461 7.864137 1.149994 2.468021 8.785956 1.149994 2.914997 9.701066 1.149994 3.328043 10.6008 1.149994 3.709151 11.47799 1.149994 4.061482 12.32555 1.149994 4.387573 13.13732 1.149994 4.68884 13.90812 1.149994 4.965901 14.63363 1.149994 5.219686 15.31001 1.149994 5.450822 15.93411 1.149994 5.659624 16.50354 1.149994 5.846282 17.01667 1.149994 6.011107 17.47252 1.149994 6.154513 17.87087 1.149994 6.277023 18.21229 1.149994 6.379348 18.49817 1.149994 6.462435 18.73074 1.149994 6.527493 18.91312 1.149994 6.546914 19.05646 1.149994 6.505058 19.14839 1.149994 6.459251 19.1927 1.149994 6.416416 19.21633 1.149994 6.376531 19.22838 1.149994 6.322405 19.23225 1.149994 6.23916 19.21045 1.149994 6.148637 19.12692 1.149994 6.078928 18.97745 1.149994 5.99009 18.78678 1.149994 5.880557 18.5525 1.149994 5.749261 18.27283 1.149994 5.595376 17.94671 1.149994 5.418293 17.57375 1.149994 5.217749 17.15414 1.149994 4.993443 16.68879 1.149994 4.745233 16.17917 1.149994 4.473207 15.62726 1.149994 4.177543 15.03554 1.149994 3.858261 14.40712 1.149994 3.51512 13.74572 1.149994 3.148386 13.05527 1.149994 2.75791 12.34036 1.149994 2.342847 11.60635 1.149994 1.902294 10.8591 1.149994 1.435936 10.10457 1.149994 0.942335 9.349849 1.149994 0.419293 8.603157 1.149994 −0.13522 7.873431 1.149994 −0.72246 7.17005 1.149994 −1.34427 6.504218 1.149994 −2.0021 5.888887 1.149994 −2.69571 5.338305 1.149994 −3.42188 4.867249 1.149994 −4.17312 4.489288 1.149994 −4.93717 4.214747 1.149994 −5.69761 4.047598 1.149994 −6.43607 3.984102 1.149994 −7.13621 4.011876 1.149994 −7.78509 4.112493 1.149994 −8.37569 4.264198 1.149994 −8.90631 4.445274 1.149994 −9.37943 4.635058 1.149994 −9.80074 4.81349 1.149994 −10.1748 4.967435 1.149994 −10.5102 5.075386 1.149994 −10.8054 5.115186 1.149994 −11.0499 5.066146 1.149994 −11.2106 4.950492 1.149994 −11.3044 4.831419 1.149994 −11.3625 4.739187 1.149994 −11.3981 4.678212 1.149994

In the above Table 1, the plane Zadim=0 corresponds to the reference plane P0 situated at the base of the profile. This plane P0 is the intersection of the stacking axis AE of the set of vanes with the axisymmetric surface of the hub, i.e. it passes via the intersection between the axis AE and the surface where it is assembled with the inner shroud. The plane Zadim=1 corresponds to the reference plane P1 situated at the top of the profile. This plane P1 is the intersection between the axis AE and the axisymmetric surface of the casing, i.e. it passes via the intersection of the axis AE with the surface where it is assembled with the outer ring.

By convention, the stacking axis AE of a vane of a nozzle, is an axis that extends in the radial direction Z and is an axis on which the various X,Y sections of the set of vanes are “stacked” when designing the set of vanes.

As mentioned at the beginning of the present description, the aerodynamic profile of the disclosure is substantially identical to the nominal profile defined in the above table, i.e. it departs from said nominal profile by very little at most, being defined in particular within an envelope of ±1 mm in a direction normal to the surface of the nominal profile, and/or having X,Y coordinates lying within a range of ±5% relative to the coordinates X,Y of the nominal profile. Also, the aerodynamic profile is positioned rotated within ±10°, particularly within ±5°, more particularly within ±3°, with respect to the stacking axis of the vane. In other words, the stagger angle may vary by ±10°, particularly by ±5°, more particularly by ±3°.

The coordinate Zadim is non-dimensional, i.e. for a point P, situated at a distance D from the plane P0 (where D is measured along the axis Z), the value of Zadim is D/H, where H represents the total height of the profile as measured between the planes P0 and P1. Naturally, in the Table 1 above, by multiplying the coordinate Zadim by the height H, it is possible to obtain the complete coordinates of the vane.

By way of example, the total height H is preferably about 123 mm±10%. By way of example, the plane P0 is situated at a distance of about 379 mm±10% from the axis A.

In the above table, the profile is characterized by fifteen section planes at constant Zadim coordinates, for which the coordinates X and Y are specified. These fifteen section planes include fifteen section planes located between Zadim=0 and Zadim=1, and thus arranged in the fluid stream, these section planes being distributed from P0 to P1. The fifteen section planes also include four section planes which are substantially outside the fluid stream (two section planes with Zadim<0, and two section planes with Zadim>1), these four section planes being provided for ensuring geometric continuity of the stacking, close to the head and the foot, respectively. In each section plane at constant coordinate Zadim, the section of the profile is given by a continuous and smooth curve, interconnecting all of the points (X,Y). In each section plane, the profile is interpolated so as to generate a uniform profile. Between the section planes, the profile is to be interpolated so as to generate a complete vane, as homogeneous as possible.

It is advantageous for the nozzle that includes the vane of the disclosure to have 136 to 156 vanes, more particularly 146 vanes, that present aerodynamic profiles as defined above. 

What is claimed is:
 1. An aerodynamic profile for a turbine vane, the profile being, when cold and in a non-coated state, substantially identical to a nominal profile determined by the Cartesian coordinates X,Y,Zadim given in Table 1, in which the coordinate Zadim is the quotient D/H, where D is the distance of the point under consideration from a reference X,Y plane situated at the base of the nominal profile, and H is the height of said profile measured from said reference plane out to the end of the vane, the measurements D and H being taken radially relative to the axis of the turbine, while the coordinate X is measured in the axial direction of the turbine.
 2. The aerodynamic profile as claimed in claim 1, wherein said profile is defined within an envelope of ±1 mm in a direction normal to the surface of the nominal profile.
 3. The aerodynamic profile as claimed in claim 1, wherein the coordinates X,Y of said profile lie within a range of ±5% relative to the coordinates X,Y of the nominal profile.
 4. The aerodynamic profile as claimed in claim 1, wherein the aerodynamic profile is positioned rotated within ±10° with respect to the radial axis of the vane, along which the coordinate Zadim is measured.
 5. The aerodynamic profile as claimed in claim 1, wherein the aerodynamic profile is positioned rotated within ±5° with respect to the radial axis of the vane, along which the coordinate Zadim is measured.
 6. The aerodynamic profile as claimed in claim 1, wherein the aerodynamic profile is positioned rotated within ±3° with respect to the radial axis of the vane, along which the coordinate Zadim is measured.
 7. The aerodynamic profile as claimed in claim 1, wherein the vane is a nozzle vane forming a part of a stator of a turbine.
 8. A turbine vane, presenting the aerodynamic profile as claimed in claim
 1. 9. A turbine, including turbine vanes presenting aerodynamic profiles as claimed in claim
 1. 10. A turbine as claimed in claim 9, including a nozzle that is stationary in rotation, having 136 to 156 vanes that present the aerodynamic profiles.
 11. A turbine as claimed in claim 9, including a nozzle that is stationary in rotation, having 146 vanes that present the aerodynamic profiles.
 12. A turbine nozzle forming a portion of a turbine stator, wherein all the vanes of the nozzle present the aerodynamic profile as claimed in claim
 1. 13. A turbine nozzle as claimed in claim 12, including 136 to 156 vanes that present the aerodynamic profiles.
 14. A turbine nozzle as claimed in claim 12, including 146 vanes that present the aerodynamic profiles. 